
where \((\sigma _k)_{k=1}^m\)  are i.i.d Rademacher random variables independent from \((Z_k)_{k=1}^m\) . Hence, additionally applying the Khintchine inequality, Lemma 4.1 in [1]}, we obtain
\(\mathbb {E} \Vert  \beta - \bar{Z}_m \Vert _1 \le \frac{2\sqrt{2\pi }}{\sqrt{m}} \sqrt{\mathbb {E} \left\Vert  Z \right\Vert _2^2} \le \frac{2\sqrt{2\pi } r_n}{\sqrt{m}} .\) 
